Recent content by silmaril89

Ok, thanks for the reply. I think I'm still a little confused, but you've put me in a particular direction to begin investigating this further.

"Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model." --https://en.wikipedia.org/wiki/C-symmetry The excerpt above seems to...

This question comes from section 2.3 of 'Quantum Field Theory' by Lewis Ryder. The discussion is on the Lie Group SU(2). He discusses the transformations of vectors under SU(2). Here it goes: consider the basic spinor \xi = \begin{pmatrix} \xi_1 \\ \xi_2 \end{pmatrix} ; \xi \to U \xi...

Homework Statement The Hamiltonian for two particles with angular momentum j_1 and j_2 is given by: \hat{H} = \epsilon [ \hat{\bf{j}}_1 \times \hat{\bf{j}}_2 ]^2, where \epsilon is a constant. Show that the Hamiltonian is a Hermitian scalar and find the energy spectrum.Homework Equations...

Normalization is tough, but I just divided by ( \theta_2 - \theta_1 ), but something tells me that isn't right.

P(\theta) = \frac{4}{\pi} \mid \sin \theta \cos \theta \mid

Yes, but the specification is that P(x,y) is only valid on a ring of radius 1 (i.e. (1,1) is not a valid point). Basically, I have the probability of an event occurring being equal to P(x,y) = \frac{4}{\pi} x y , but the issue is that I don't know what the probability for the event to occur if...

I'm sure. I understand how it doesn't make much sense to think of mass as a function of position. I have another question that led me to this one. The real question is about probability density. I have that the probability of some thing occurring to be P(x,y) = \frac{4}{\pi} x y , but I want...

Let's say you have the mass of an object as a function of position, how would I go about finding the mass density as a function of position? I want a general answer, one that doesn't assume the mass has uniform density (that would be trivial). As an example, can you solve this? Say you...

Right, I guess I was just trying to prove a point that it would be non-zero. Correct me if I'm wrong, but I think the acceleration in the \hat{r} direction for constant r = R should be, \textbf{a} = -(R \dot{\theta}^2 + R \dot{\phi}^2\sin^2{\theta}) \hat{r} It's too bad the solution...

No, if it's moving on a sphere, then it's acceleration should be \frac{v^2}{r} \hat{r}.

If you look at the solution manual, it doesn't say we simply ignore it since it's irrelevant. It actually says that the total force in the \hat{r} direction sums to zero. This doesn't make sense.

That certainly helps me understand how F_\theta and F_\phi could be non-zero, but how could F_r be zero?

Problem 2-2 from "Classical Dynamics of Particles and Systems" By Thornton and Marion is stated as follows: A particle of mass m is constrained to move on the surface of a sphere of radius R by an applied force \textbf{F}(θ, \phi). Write the equation of motion. Initially I felt that the...

@jtbell Thanks, that again makes sense. The use of equations makes it quite easy to see what is happening. Is it possible to show me with equations what it was that I was doing? You mention that you use either the work done by a conservative force, or the potential energy associated with that...